In this note, we apply white noise analysis to infinitely divisible distributions on a real Gel'fand triple E ⊂ H ⊂ E *. We first introduce an index, called Hida index, for a measure on E ⊂ H ⊂ E *. And then, under some mild conditions, we obtain a general inequality which indicates a connection between the Hida index of an infinitely divisible distribution on E ⊂ H ⊂ E * and that of its Lévy measure. Finally we prove that the Hida index of the standard compound Poisson distribution on E ⊂ H ⊂ E * is exactly 1. © 2005 Elsevier Inc. All rights reserved.
Wang, C., Qu, M., & Chen, J. (2006). A white noise approach to infinitely divisible distributions on Gel’fand triple. Journal of Mathematical Analysis and Applications, 315(2), 425–435. https://doi.org/10.1016/j.jmaa.2005.09.030